We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations ͓x i ,p j ͔ϭiប͓(1ϩ␤ p 2 )␦ i j ϩ␤Јp i p j ͔. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relations which appear in perturbative string theory. Our solutions illustrate how certain features of string theory may manifest themselves in simple quantum mechanical systems through the modification of the canonical commutation relations. We discuss whether such effects are observable in precision measurements on electrons trapped in strong magnetic fields.

We continue our investigation of the phenomenological implications of the ''deformed'' commutation relations ͓x i ,p j ͔ϭiប͓(1ϩ␤ p 2 )␦ i j ϩ␤Јp i p j ͔. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.

We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation ͓x i ,p j ͔ϭiប͓(1ϩ␤ p 2 )␦ i j ϩ␤Јp i p j ͔. We point out that this relation, which is an example of a UV/IR relation, implies the finiteness of the cosmological constant. While our result does not solve the cosmological constant problem, it does shed new light on the relation between this outstanding problem and UV/IR correspondence. We also point out that the blackbody radiation spectrum will be modified at higher frequencies, but the effect is too small to be observed in the cosmic microwave background spectrum.

No abstract

We study physics potential of placing a far detector in the east coast of Korea, where the off-axis neutrino beam from J-PARC at Tokai village for the T2K project has significant intensity at a few GeV range. In particular, we examine the capability of determining the mass hierarchy pattern and the CP phase of the lepton-flavor-mixing matrix when a 100 kt waterČerenkov detector is placed at various locations in Korea for the off-axis beam (OAB) of 2.5 • and 3.0 • at the Super-Kamiokande site. The best results are found for a combination of 3.0 • OAB at SK (L = 295km) and 0.5 • OAB at L = 1000km, where the mass hierarchy pattern can be determined at 3-σ level for sin 2 2θ RCT > ∼ 0.05 (0.06) when the hierarchy is normal (inverted), after 5 years of running (5 × 10 21 POT). We also find that the leptonic CP phase, δ MNS , can be constrained uniquely, without invoking anti-neutrino beams, as long as the mass hierarchy pattern is determined. Those results are obtained by assuming that the charged current quasi-elastic events can be separated from the other backgrounds with high efficiency, the neutrino energy can be reconstructed with a hundred MeV uncertainty, and the earth matter density along the baseline can be determined with 3% accuracy. *